Upper critical field of $\mathrm{K}{\mathrm{Fe}}_2{\mathrm{As}}_2$ under pressure: A test for the change in the superconducting gap structure

We report measurements of electrical resistivity under pressure to $5.8$ GPa, magnetization to $6.7$ GPa, and ac susceptibility to $7.1$ GPa in $\mathrm{K}{\mathrm{Fe}}_2{\mathrm{As}}_2$. The previously reported change of slope in the pressure dependence of the superconducting transition temperature $T_c\left(p\right)$ at a pressure $p^{*}\sim 1.8$ GPa is confirmed, and $T_c\left(p\right)$ is found to be nearly constant above $p^{*}$ up to $7.1$ GPa. The $T\text{−}p$ phase diagram is very sensitive to the pressure conditions as a consequence of the anisotropic uniaxial pressure dependence of $T_c$. Across $p^{*}$, a change in the behavior of the upper critical field is revealed through a scaling analysis of the slope of $H_{c_2}$ with the effective mass as determined from the $A$ coefficient of the $T^2$ term of the temperature-dependent resistivity. We show that this scaling provides a quantitative test for the changes of the superconducting gap structure and suggests the development of a $k_z$ modulation of the superconducting gap above $p^{*}$ as a most likely explanation.

Figure 1

Superconducting phase diagram for ${\mathrm{KFe}}_2{\mathrm{As}}_2$ determined from our resistivity and ac susceptibility measurements [28]. For the latter, filled symbols are used when pressure was applied on liquid helium, whereas open symbols are used when pressure was applied on solid helium (at 10 K). The dashed line is a guide to the eye which does not use the two data points where the pressure was applied on solid helium. The data from Refs. [9, 16] are also shown.

Figure 2

Temperature dependence of the upper critical field $H_{c_2}$ at different pressures. The data were determined using a resistive transition offset criteria ($\rho =0$, see Ref. [25]). We note that, unlike the use of the transition midpoint criteria, the chosen offset criteria agree more closely with ambient pressure specific heat measurements [51]. The inset shows the pressure dependence of $H_{c_2}$ at $0.5$ K.

Figure 3

Electrical resistivity $\rho$ of ${\mathrm{KFe}}_2{\mathrm{As}}_2$ at different pressures at low temperatures as a function of $T^2$. The dashed lines show fits of the resistivity to a Fermi liquid behavior $\rho ={\rho }_0+A{T}^2$. The pressure dependence of the $A$ coefficient is shown in the inset. The dashed line represents $A\left(0\right)/{(1+\beta p)}^2$ where $\beta =0.16\left(1\right) {\mathrm{GPa}}^{-1}$.

Figure 4

Plot of $(-d{\mu }_0{H}_{c_2}/dT{|}_{T_c})/T_c$ vs the $A$ coefficient of resistivity. Each point corresponds to a different pressure. All measured points fall onto two lines of different slope corresponding to $p<p*$ and $p>p*$. The two insets show a schematic gap structure with the appearance of a modulation along $k_z$ above $p^{*}$.